“Lizzie Borden took an axe, and gave her mother 40 whacks. When she saw what she had done, she gave her father 41 …” A century and a quarter after Andrew and Abby Borden were murdered with a hatchet on a sweltering Massachusetts morning, the skipping rhyme still resonates and the case of Lizzie Borden – arrested, tried and acquitted by a jury unable to believe a woman could do such a thing – continues to fascinate. It has been immortalised in countless books, a TV series, a short story by Angela Carter; a film starring Chloë Sevigny and Kristen Stewart is due to be released this year. The house where the killings took place is now a B&B-cum-museum, with the most requested room the one where Abby was murdered. Tours run every hour; free for children six and under. You can buy a Lizzie Borden doll.

Sarah Schmidt’s debut novel is a feverish reimagining of the day of the murders, the leadup and aftermath, told by four voices: Lizzie, her older sister Emma, the maid Bridget, and a dangerous stranger called Benjamin, who is linked to the family by Lizzie and Emma’s maternal uncle John.

Many theories about the motivations for the killings have been advanced over the decades. Abby was actually Lizzie’s stepmother, her mother having died when she was very young, and their relationship was less than cordial. Now in her 30s but stuck at home, an eternal spinster, Lizzie must have resented her rich but miserly father settling property on Abby’s relatives; or maybe it was his recent slaughter of her beloved pet pigeons that sent her over the edge. Thriller writer Ed McBain proposed a discovered lesbian tryst between Lizzie and Bridget. Or perhaps Lizzie wasn’t the killer after all: there was talk at the time of a previous break-in, and murmurings of poisoning after sickness tore through the house. The murders have been pinned on the badly treated maid, on a spurned illegitimate son of Andrew Borden, on the uncle who seldom visited but just happened to be there at the time.

Schmidt is less interested in contriving a new version of what “really” happened on that fateful morning in 1892 than in plunging the reader into a claustrophobic nexus of family resentments and frustrations, probing obsessively at the faultline between love and hate. At the heart of the novel is the relationship between Lizzie and Emma. “None of this would have happened if she hadn’t left me in the house,” declares Lizzie. Emma had been staying with a friend, desperate to escape the needy, domineering younger sister who demands that the door between their bedrooms be always kept open, consigning Emma to a cubicle within her own room as though swallowing her whole. “I would wake with my sister in my mouth,” says Emma, “hair strands, a taste of sour milk, like she was possessing me.” As the motherless girls age into women, under the thumb of their controlling, critical father, childhood affection for their stepmother curdles into contempt. The household has reached an emotional impasse, with even Bridget, yearning for her home in Ireland, trapped by the savings tin Mrs Borden has confiscated. “You shouldn’t be allowed to just leave!” shrieks Abby, who relieves her own feelings by repeatedly punching herself in the stomach.

Nouns are twisted into verbs as blood 'rivers' down necks; heat rises, everything that was once fresh rots

Something has to give. The narrative lurches back and forth, with Lizzie giving us impressionistic snatches of her movements on the day of the murders, narrated in a fervent babble somewhere between babytalk and the halting urgency of Emily Dickinson. Nouns are twisted into verbs as blood “rivers” down necks; heat rises, everything that was once fresh rots with the “death smells” of summer and characters repeatedly vomit up spoiled food from the “deep-pit” of themselves. It’s sensory overload, and overwhelming. All remark on the stink and stifling proximity of others, “the smell of sour yoghurt snaking out from somewhere inside her”, or the “air coming in and out like an ocean tide, smelling of old meat and butter”, as though oppressed by each other’s very life’s breath. They wonder, too, what they and others look like on the inside, beneath the sweaty flesh and many layers of dirty clothes: in the case of Mr and Mrs Borden, hacked about so that their brain matter and eye jelly is exposed, they find out. Characters leave what’s inside them – puke, rotten teeth – abandoned in corners, physical manifestations of the simmering rage and soured love that cannot be contained.

The blurring of voices and perceptions, particularly between Lizzie and Benjamin, and obsessive repetition of words and symbols only add to the irresistible momentum and fevered intensity of the book: part fairytale, part psychodrama. “Some men scare easy, some men are the scare. I knew what I was,” says Benjamin, a blankly terrifying agent of chaos who could be a projection of Lizzie’s most violent urges.

At the same time, much backstory is cleverly withheld: there are hints at Lizzie’s instability, but we bring our own assumptions to her character; creepy uncle John is referred to repeatedly as “that man”, with a shiver of disgust, but we find out very little about him; mysterious Benjamin leaves us guessing. We get only glimpses into the particular hell of the Borden household; the fact that we can fill in the blanks from our own darkest places draws us closer, more uncomfortably, in. Schmidt’s unusual combination of narrative suppression and splurge makes for a surprising, nastily effective debut. Neighbours, doctor, police: visitors to the Borden house in the aftermath of the murders react with incredulity. “I don’t think I believe it myself,” says Lizzie.

•See What I Have Done is published by Tinder Press. To order a copy for £11.04 (RRP £12.99) go to bookshop.theguardian.com or call 0330 333 6846. Free UK p&p over £10, online orders only. Phone orders min p&p of £1.99.